Why random matrices share universal processes with interacting particle systems?
Mathematical Physics
2013-12-17 v2 Statistical Mechanics
math.MP
Probability
Abstract
In these lecture we explain why limiting distribution function, like the Tracy-Widom distribution, or limit processes, like the Airy_2 process, arise both in random matrices and interacting particle systems. The link is through a common mathematical structure on an interlacing structure, also known as Gelfand-Tsetlin pattern, that appears for specific models in both fields.
Keywords
Cite
@article{arxiv.1312.1126,
title = {Why random matrices share universal processes with interacting particle systems?},
author = {Patrik L. Ferrari},
journal= {arXiv preprint arXiv:1312.1126},
year = {2013}
}
Comments
Extended lecture notes of the ICTP minicourse in Trieste, September 2013. 45 pages, 6 figures; Minor corrections